This paper describes the shape optimization of NASA rotor 37 and rotor and stator blades in a single-stage transonic axial compressor.Shape optimization of the blades operating at the design flow condition has been performed using the response surface method and three-dimensional Navier-Stokes analysis.Thin-layer approximation is introduced to the Navier-Stokes equations

and an explicit Runge-Kutta scheme is used to solve the governing equations.The three design variables

blade sweep

lean and skew

are introduced to optimize the three-dimensional stacking line of the blades.The objective function of the shape optimization is an adiabatic efficiency.Throughout the optimization of rotor and stator blades

optimal blade shape can be obtained.It is noted the increase of adiabatic efficiency by optimization of the blade shape with the stacking line in the single-stage transonic axial compressor is more effective in a rotor blade rather than a stator blade because of the large deformation of blade shape in the stator blade.